AN INNOVATIVE APPROACH IS PROPOSED TO DEVELOP AN ANALYSIS FOR LIQUID FLOWS WITH VAPOR BUBBLES, SUCH AS THOSE WHICH OCCUR IN BEARINGS, SEALS, AND PUMPS IN LIQUID ROCKET ENGINES. THE APPROACH IS BASED ON A COMBINED EULERIAN-LAGRANGIAN ANALYSIS, IN WHICH THE CONTINUOUS (LIQUID) PHASE IS TREATED BY SOLVING A SYSTEM OF EULERIAN CONSERVATION EQUATIONS, WHILE THE DISCRETE (VAPOR BUBBLE) PHASE IS DEALT WITH BY INTEGRATING LAGRANGIAN EQUATIONS OF MOTION. VAPOR BUBBLES OF CHANGING SIZE CAN BE ACCOMMODATED EASILY BY THIS ANALYSIS, AND THE PROCESSES OF VAPOR BUBBLE FORMATION, GROWTH, COALESCENCE, AND COLLAPSE CAN BE SIMULATED BY INCLUDING APPROPRIATE MODELS. BUBBLE MASS, MOMENTUM, AND ENERGY INTERCHANGE SOURCE TERMS IN THE EULERIAN CONSERVATION EQUATIONS ACCOUNT FOR THE EFFECTS OF BUBBLE MOTION AND OTHER BUBBLE PROCESSES ON THE CONTINUOUS (LIQUID) PHASE. THE RESULTING PROCEDURE WILL BE CAPABLE OF ADDRESSING THE EFFECT OF VARIOUS PARAMETERS THAT ARE OF IMPORTANCE IN THE DESIGN OF BEARINGS, SEALS, AND PUMPS.